Abstract mathematical treatment of relativistic phenomena

This preprint concerns a mathematically rigorous treatment of an interesting physical phenomenon in relativity theory. We would like to draw the reader's attention particularly to the abstract mathematical formalism of relativity (which was developed in full detail in \cite{matolcsi2}). This treatment allows all mathematically oriented readers to understand relativity without feeling the awkward ambiguities that are so common after reading a standard text on relativity. In the extensive literature dealing with the relativistic phenomenon of Thomas rotation several methods have been developed for calculating the Thomas rotation angle of a gyroscope along a circular world line. One of the most appealing methods \cite{rindler}, however, subsequently led to a contradiction in \cite{herrera} when three different Thomas rotation angles were obtained for the same circular world line. In this paper we resolve this contradiction by rigorously examining the theoretical background and the limitations of the principle of \cite{rindler}.